Research Group: Numerical Mathematics and Scientific Computing
Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Tel: +49(0) 30 20372 446
Fax: +49(0) 30 2044975
I'm a scientific staff member of the Weierstrass Institute for Applied
Analysis and Stochastics (WIAS) in the research group of
Numerical Mathematics and Scientific Computing. My work is
supported under the research project pdelib of WIAS.
I work in the field of automatic mesh generation,
which is a topic about how to partition a geometric domain into a set of simple
(non-overlapping) cells. It has wide variaty of applications:
mathematical modeling, computer-aided design, visualizations, and so
on. It combines different topics from mathematics, computer science, and
engineering. It principally requires the studies of discretizing a
continuous space in both of its topology and geometry. My primary
investigations are the existence and the complexity of such a
discretization. Many questions of this study stem from problems in
discrete and combinatorial geometry.
The goal of my work is to develope efficient algorithms to
automatically generate meshes from arbitrary geometry. It is motivated
by solving partial
differential equations using numerical methods such as finite element
and finite volume methods. I focus on three-dimensional
tetrahedral mesh generation. We're developing algorithms to
efficiently generate tetrahedral meshes satisfying the Delaunay
criterion, which have many nice properties which are important for efficient numerical schemes. We're developing techniques to construct constrained
Delaunay tetrahedralizations, quality conforming Delaunay
tetrahedralizations for three-dimensional geometries with arbitrarily
I'm also writing a computer program, TetGen, which is used to implement
state-of-the-art methods and algorithms for constructing Delaunay
tetrahedralizations and quality tetrahedral meshes. It is one of the
best ways to connect "methods" and "results". On the other hand, to
provide a robust and efficient meshing tool for solving practical
problems in engineering is also very meaningful.
Here is a list of my recent publications.
Here is my Ph.D thesis: Three dimensional boundary confomring Delaunay mesh
generation, Institute of Mathematics, Technische Univerisität Berlin, 2008.
- H. Si. TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw., 41(2):11:1--11:36, February 2015.
- J. R. Shewchuk and H. Si. Higher-Quality Tetrahedral Mesh Generation for Domains with Small Angles by Constrained Delaunay Refinement . In Proceedings of the Thirtieth Annual Symposium on Computational Geometry, SOCG 2014, pages 290--299, New York, NY, USA, 2014. ACM.
- H. Si and J. R. Shewchuk. Incrementally constructing and updating constrained delaunay tetrahedralizations with finite-precision coordinates. Engineering with Computers, 30(2):253--269, 2014. [pdf]
- H. Si, K. Gärtner, 3D boundary recovery by
constrained Delaunay tetrahedralization. Int. J. Numer. Meth. Engrg. 85:
- H. Si, J. Fuhrmann, K. Gärtner, Boundary conforming
Delaunay mesh generation. Comput. Math. Phys. 50
- H. Si, Constrained Delaunay tetrahedral mesh generation and
refinement. Finite elements in Analysis and Design, 46
- F. Drechsler, C.H. Wolters, T. Dirkes, H. Si, L. Grasedyck, A
full subtraction approach for finite element method based source
analysis constrained Delaunay tetrahedralization, NeuroImage,
- H. Si, An analysis of Shewchuk's Delaunay refinement
algorithm, In Proc. 18th International Meshing Roundtable, 2009. [pdf]
- H. Si, Adaptive tetrahedral mesh generation by constrained
Delaunay refinement, Int. J. Numer. Meth. Engrg. 75:
Corrections: The Lemma 3.3.2 and and the Theorem 3.3.4 in my
Ph.D thesis are
wrong. The correct versions are found in the paper "An analysis of Shewchuk's Delaunay refinement
algorithm, In Proc. 18th International Meshing Roundtable, 2009."
TetGen is a
computer program to generate exact Delaunay tetrahedralizations, exact
constrained Delaunay tetrahedralizations, and quality tetrahedral
meshes. The latter are quality conforming Delaunay and nicely graded. The source code as well
as documentation are freely available.
a small graphic program used to visualize tetrahedral meshes and
piecewise linear complexes. It directly shows the input and output
objects (in files) of TetGen on screen. It also has many features for
understanding and analysing the viewing objects. It dumps screen
contents in high quality encapsulated postscript format. The
executable file (on Unix/Linux platforms) is freely available.
A short biography
I was born and grew up in Hangzhou, a city famous for its natural beauty and
historical culture in the Zhejiang province of China. I received my B.E. degree in Electrical Engineering of the Hangzhou
University (now merged in Zhejiang University) in July, 1994, and my
M.S. degree in Computer Science of the Zhejiang University in March,
2002. In between of my two college studies, I've worked as an
electrical engineer and a software developer
for five years. I jointed WIAS Berlin in
October, 2002 and have been working here since then. In August 2008, I got my Ph.D from the Institute für Mathematik
Univerisität Berlin under the supervisor of Prof. Günter
Ziegler and Herbert